Microfluidic devices with integrated resistive heater electrodes including systems and methods for controlling and measuring the temperatures of such heater electrodes

ABSTRACT

The invention relates to methods and devices for control of an integrated thin-film device with a plurality of microfluidic channels. In one embodiment, a microfluidic device is provided that includes a microfluidic chip having a plurality of microfluidic channels and a plurality of multiplexed heater electrodes, wherein the heater electrodes are part of a multiplex circuit including a common lead connecting the heater electrodes to a power supply, each of the heater electrodes being associated with one of the microfluidic channels. The microfluidic device also includes a control system configured to regulate power applied to each heater electrode by varying a duty cycle, the control system being further configured to determine the temperature each heater electrode by determining the resistance of each heater electrode.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of Provisional Patent ApplicationSer. No. 60/968,760, filed Aug. 29, 2007, which is incorporated hereinby reference in its entirety.

BACKGROUND

1. Field of Invention

The present invention relates to microfluidic devices and temperaturecontrol of the microfluidic devices for performing biological reactions.More specifically, the present invention relates to systems and methodsfor determining and controlling the temperature of integrated thin filmresistive heater elements in the microfluidic device.

2. Discussion of the Background

The detection of nucleic acids is central to medicine, forensic science,industrial processing, crop and animal breeding, and many other fields.The ability to detect disease conditions (e.g., cancer), infectiousorganisms (e.g., HIV), genetic lineage, genetic markers, and the like,is ubiquitous technology for disease diagnosis and prognosis, markerassisted selection, identification of crime scene features, the abilityto propagate industrial organisms and many other techniques.Determination of the integrity of a nucleic acid of interest can berelevant to the pathology of an infection or cancer.

One of the most powerful and basic technologies to detect smallquantities of nucleic acids is to replicate some or all of a nucleicacid sequence many times, and then analyze the amplification products.Polymerase chain reaction (PCR) is a well-known technique for amplifyingDNA. With PCR, one can produce millions of copies of DNA starting from asingle template DNA molecule. PCR includes phases of “denaturation,”“annealing,” and “extension.” These phases are part of a cycle which isrepeated a number of times so that at the end of the process there areenough copies to be detected and analyzed. For general detailsconcerning PCR, see Sambrook and Russell, Molecular Cloning—A LaboratoryManual (3rd Ed.), Vols. 1-3, Cold Spring Harbor Laboratory, Cold SpringHarbor, N.Y. (2000); Current Protocols in Molecular Biology, F. M.Ausubel et al., eds., Current Protocols, a joint venture between GreenePublishing Associates, Inc. and John Wiley & Sons, Inc., (supplementedthrough 2005) and PCR Protocols A Guide to Methods and Applications, M.A. Innis et al., eds., Academic Press Inc. San Diego, Calif. (1990).

The PCR process phases of denaturing, annealing, and extension occur atdifferent temperatures and cause target DNA molecule samples toreplicate themselves. Temperature cycling (thermocyling) requirementsvary with particular nucleic acid samples and assays. In the denaturingphase, a double stranded DNA (dsDNA) is thermally separated into singlestranded DNA (ssDNA). During the annealing phase, primers are attachedto the single stranded DNA molecules. Single stranded DNA molecules growto double stranded DNA again in the extension phase through specificbindings between nucleotides in the PCR solution and the single strandedDNA. Typical temperatures are 95° C. for denaturing, 55° C. forannealing, and 72° C. for extension. The temperature is held at eachphase for a certain amount of time which may be a fraction of a secondup to a few tens of seconds. The DNA is doubled at each cycle; itgenerally takes 20 to 40 cycles to produce enough DNA for theapplications. To have good yield of target product, one has toaccurately control the sample temperatures at the different phases to aspecified degree.

More recently, a number of high throughput approaches to performing PCRand other amplification reactions have been developed, e.g., involvingamplification reactions in microfluidic devices, as well as methods fordetecting and analyzing amplified nucleic acids in or on the devices.Thermal cycling of the sample for amplification is usually accomplishedin one of two methods. In the first method, the sample solution isloaded into the device and the temperature is cycled in time, much likea conventional PCR instrument. In the second method, the sample solutionis pumped continuously through spatially varying temperature zones. See,for example, Lagally et al. (Analytical Chemistry 73:565-570 (2001)),Kopp et al. (Science 280:1046-1048 (1998)), Park et al. (AnalyticalChemistry 75:6029-6033 (2003)), Hahn et al. (WO 2005/075683),Enzelberger et al. (U.S. Pat. No. 6,960,437) and Knapp et al. (U.S.Patent Application Publication No. 2005/0042639).

Many detection methods require a determined large number of copies(millions, for example) of the original DNA molecule, in order for theDNA to be characterized. Because the total number of cycles is fixedwith respect to the number of desired copies, the only way to reduce theprocess time is to reduce the length of a cycle. Thus, the total processtime may be significantly reduced by rapidly heating and cooling samplesto process phase temperatures while accurately maintaining thosetemperatures for the process phase duration.

Accordingly, what is desired is a system and method for rapidly andaccurately changing process temperatures in PCR processes.

SUMMARY

The present invention relates to systems and methods for determining andcontrolling the temperature of integrated thin film resistive heaterelements in a microfluidic device for microfluidic thermal cycling.

In one aspect, the present invention provides a method for determiningthe temperature of each of a plurality of multiplexed heater electrodes,wherein the heater electrodes are part of a multiplex circuit sharing acommon lead connecting the electrodes to a power supply. In oneembodiment, the method includes: (a) independently measuring a voltagedrop of each heater electrode in series with the common lead and storinga common power voltage drop data for each of the heater electrodes; (b)disconnecting the power supply from the common lead; (c) connecting thepower supply to each of one or more of the heater electrodes, whereinthe power supply is connected to one of the heater electrodes at a time;(d) while the power supply is connected to a heater electrode, isolatingat least one other heater electrode from all other heater electrodes ofthe multiplex circuit except the heater electrode connected to powersupply, measuring an isolated voltage drop at each isolated heaterelectrode, and storing isolated voltage drop data for each isolatedheater electrode; (e) computing the resistance of each of the pluralityof multiplexed heater electrodes by solving for the resistance of eachheater electrode based at least in part on the stored common powervoltage drop data and the stored isolated voltage drop data; and (f)deriving the temperature of each of the plurality of multiplexed heaterelectrodes from the computed resistance of each electrode.

In another embodiment, the multiplex circuit includes n heaterelectrodes, step (c) comprises connecting the power supply to heaterelectrode n−1, and step (d) comprises isolating heater electrode n andmeasuring an isolated voltage drop at heater electrode n. In still otherembodiments, step (e) includes solving a linear system of equations forthe resistance of each of the plurality of heater electrodes and aparasitic resistance of the common lead.

In another embodiment, the multiplex circuit includes n heaterelectrodes, step (c) comprises connecting the power supply to heaterelectrode 1, and step (d) comprises isolating heater electrode n andmeasuring an isolated voltage drop at heater electrode n, and whereinthe method further comprises, prior to performing steps (e) and (f)repeating step (c) for heater electrode n−1 and then repeating step (d)for heater electrode n.

In another embodiment, step (e) comprises solving a linear system ofequations for the resistance of each of the plurality of heaterelectrodes, a parasitic resistance of the common lead, and the sum ofthe parasitic resistances of all heater electrode channels. In stillother embodiments, the multiplex circuit comprises n heater electrodes,step (c) comprises sequentially connecting the power supply to eachheater electrode i, wherein i=1 to (n−1), and step (d) comprises, foreach heater electrode i connected to the power supply, isolating heaterelectrode i+1 and measuring an isolated voltage drop at heater electrodei+1. In other embodiments, step (e) includes solving an overdeterminedsystem with optimization techniques.

In another embodiment, the multiplex circuit comprises n heaterelectrodes, step (c) comprises sequentially connecting the power supplyto each heater electrode i, wherein i=1 to (n−1), and step (d)comprises, for each heater electrode i connected to the power supply,isolating heater electrode i+1 and measuring an isolated voltage drop atheater electrode i+1, and wherein the method further comprises, prior toperforming steps (e) and (f), repeating step (c) by sequentiallyconnecting the power supply to each heater electrode i+1, wherein i=1 to(n−1) and then repeating step (d) by, for each heater electrode i+1connected to the power supply, isolating heater electrode i andmeasuring an isolated voltage drop at heater electrode i.

In another embodiment, the multiplex circuit comprises n heaterelectrodes, step (c) comprises connecting the power supply to heaterelectrode n, and step (d) comprises, while heater electrode n isconnected to the power supply, sequentially isolating heater electrodei, wherein i=1 to (n−1) and measuring an isolated voltage drop at eachheater electrode i. In this embodiment, step (e) may include solving anoverdetermined system with optimization techniques.

In yet another embodiment, the multiplex circuit comprises n heaterelectrodes, step (c) comprises sequentially connecting the power supplyto every other heater electrode i, wherein i=1 to (n−1) incremented by2, and step (d) comprises, for each heater electrode i connected to thepower supply, isolating heater electrode i+1 and measuring an isolatedvoltage drop at each heater electrode i+1. In this embodiment, step (e)comprises solving an overdetermined system with optimization techniques.

In another aspect, the method of present invention is provided whereinpower applied to a heater electrode is regulated by varying the dutycycle of a pulse width modulation (PWM). In one embodiment, measuring avoltage drop at a heater electrode includes: (a) applying a fixedvoltage across a heater channel including the heater electrode, aswitching element for selectively opening or closing the channel todefine the duty cycle, and a high resistance shunt around the switchingelement; (b) closing the channel with the switching element for a periodtime corresponding to a power-on portion of a desired duty cycle andpassing current to the heater electrode through the closed switch andthe shunt; (c) while the circuit is closed, measuring a power-on voltagedrop across the heater electrode; (d) opening the circuit with theswitching element for period of time corresponding to a power-offportion of the desired duty cycle, and passing current to the heaterelectrode exclusively through the shunt; and (e) while the circuit isopened, measuring a power-off voltage drop across the heater electrode.

In another aspect, the present invention provides a microfluidic devicefor performing biological reactions. In one embodiment, the microfluidicdevice includes a microfluidic chip having a plurality of microfluidicchannels and a plurality of multiplexed heater electrodes, wherein theheater electrodes are part of a multiplex circuit including a commonlead connecting the heater electrodes to a power supply, each of theheater electrodes being associated with one of the microfluidicchannels. The microfluidic device also includes a control systemconfigured to regulate power applied to each heater electrode by varyinga duty cycle, the control system being further configured to determinethe temperature each heater electrode by determining the resistance ofeach heater electrode.

In another embodiment, the control system of the microfluidic device isfurther configured to selectively switch the power supply from thecommon lead to one or more of the heater electrodes to measure parasiticresistance within the multiplex circuit. In other embodiments, themicrofluidic device further includes switching elements associated witheach heater electrode and wherein the control system is furtherconfigured to control the switching elements to selectively remove oneor more heater elements from the multiplex circuit to facilitateisolated measurements of voltage drops across one or more heaterelements. In other embodiments, the switching elements comprisetransistors. In still other embodiments, the switching elements comprisea primary switch and a level shifting switch to minimize the resistanceof the primary switch.

In other embodiments, the control system of the microfluidic device isfurther configured to heat the heater electrodes by pulse widthmodulation.

The above and other embodiments of the present invention are describedbelow with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments of the presentinvention. In the drawings, like reference numbers indicate identical orfunctionally similar elements. Additionally, the left-most digit(s) ofthe reference number identifies the drawing in which the referencenumber first appears.

FIG. 1 depicts a graph illustrating a temperature versus time PCRprofile.

FIG. 2 depicts a perspective view of a microfluidic device embodyingaspects of the present invention.

FIG. 3 depicts an exploded perspective view of the microfluidic deviceof FIG. 2.

FIG. 4 depicts a partial perspective view of the microfluidic device ofFIG. 2 with a portion of the device shown enlarged.

FIG. 5 depicts a block diagram illustrating the various functional andcontrol regions of a microfluidic device.

FIG. 6 depicts representative pulse width modulation (PWM) controlprofiles for achieving various temperatures in the resistive heaterelectrodes of the microfluidic device.

FIG. 7 depicts PWM profiles for an eight-channel microfluidic device,wherein the eight resistive heater electrodes are electrically driven ina multiplexed sequence.

FIG. 8 depicts PWM profiles for a differential drive method forelectrically driving microfluidic thin film resistive heaters.

FIG. 9 depicts a representative thermal response to PWM drive signals oftwo microfluidic heater channels.

FIG. 10 depicts a flow chart showing a heater calibration method.

FIG. 11 depicts a flow chart showing a PWM control method wherebycalibration values are stored and utilized to compute optimum PWMconditions.

FIG. 12 depicts a circuit enabling temperature measurements in aresistive heater electrode during both the power-off and power-onportions of a PWM duty cycle.

FIG. 13 depicts three different duty cycle profiles, wherein each dutycycle ends at about the same time so there is a period during whichpower is off for all heaters of a multiplexed system.

FIG. 14 depicts a resistive network of a microfluidic device withmultiplexed resistive heaters, wherein the heater electrodes are usedfor both heating and temperature measurement.

FIG. 15 depicts a diagram of a circuit configured to selectivelydisconnect a common lead from a power supply, selectively connect any ofthe resistive heaters channels to the power supply, or selectivelyremove any of the heater channels from the multiplex circuit.

FIG. 16 depicts a flow chart showing a representative embodiment of amethod for determining the temperatures of a plurality of multiplexedheaters.

FIG. 17 depicts a flow chart showing a first alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 18 depicts a flow chart showing a second alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 19 depicts a flow chart showing a third alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 20 depicts a flow chart showing a fourth alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 21 depicts a flow chart showing a fifth alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 22 depicts a flow chart showing a method for PWM closed-loopcontrol of a resistive heater.

FIG. 23 depicts a flow chart showing a method for analog closed-loopcontrol of a resistive heater.

FIG. 24 depicts a flow chart showing a method for PWM closed-loopcontrol for heating different resistive heaters differently to accountfor manufacturing variations or temperature gradients.

FIG. 25 depicts a flow chart showing a method for open-loop control of aresistive heater electrode.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Polymerase chain reaction (PCR) is one of the most common and criticalprocesses in molecular diagnostics and other genomics applications thatrequire DNA amplification. In PCR, target DNA molecules are replicatedthrough a three phase temperature cycle of denaturation, annealing, andextension. In the denaturation step, double stranded DNA is thermallyseparated into single stranded DNA. In the annealing step, primershybridize to single stranded DNA. In the extension step, the primers areextended on the target DNA molecule with the incorporation ofnucleotides by a polymerase enzyme.

Typical PCR temperatures are 95° C. for denaturation, 55° C. forannealing, and 72° C. for extension. The temperature at a step may beheld for an amount of time from fractions of a second to severalseconds, as shown in FIG. 1. In principle, the DNA doubles in amount ateach cycle, and it takes approximately 20 to 40 cycles to complete adesired amount of amplification. To have good yield of target product,one has to control the sample temperatures at each step to the desiredtemperature for each step. To reduce the process time, one has to heatand cool the samples to desired temperature very quickly, and keep thosetemperatures for the desired length of time to complete the synthesis ofthe DNA molecules in each cycle. This can be accomplished using amicrofluidic chip and thin-film heaters.

As shown in FIGS. 2 and 3, a microfluidic device 200 embodying aspectsof the present invention may comprise several microfluidic channels 202extending across a substrate 201. Each channel 202 may include one ormore inlet ports 203 (the illustrated embodiment shows three inlet ports203 per channel 202) and one or more outlet ports 205 (the illustratedembodiment shows one outlet port 205 per channel 202). Each channel maybe subdivided into first portion extending through a PCR thermal zone204 (as described below) and a second portion extending through athermal melt zone 206 (as described below). A sipper 208 can be used todraw liquid into the several microfluidic channels 202.

The microfluidic device 200 further includes heater elements in the formof thin film resistive heaters 212. In one embodiment, a heater element212 is associated with each microfluidic channel 202 and may be locatedbeneath the microfluidic channel 202. Each heater element 212 comprisestwo heater sections: a PCR heater 212 a section in the PCR zone 204 anda thermal melt heater section 212 b in the thermal melt zone 206. In oneembodiment, heater electrodes 210 provide electrical power to theseveral thin-film heaters 212 a and 212 b. In the embodiment shown inFIG. 2, the microfluidic device has separate electrical circuits andcontacts for controlling independently the temperature of eachmicrofluidic channel in the PCR and thermal melt zones 204, 206. In thisillustrated embodiment, each area has eight microfluidic channels andeight heaters, with eight individual contacts per zone plus a commonelectrical contact for each zone. Embodiments having other than eightchannels are contemplated as well.

As shown in FIG. 3, the microfluidic device 200 can comprise severaldifferent layers. The microfluidic channels 202 can be etched in achannel layer 302. According to some embodiments, the channel layer 302may comprise fused silica and have a thickness of about 200 μm. Ofcourse, other layer thicknesses may be used as well. A polymer gluelayer 304 may connect the channel layer 302 to a protective layer 306.According to some embodiments of the present invention, the protectivelayer is formed from SiO₂ and has a thickness of approximately 1-2 μm.Glue layer 304 may comprise sheet material with features formed thereincorresponding to the channels 202 and ports 203, 205. Alternativeadhesive layers may be formed by UV curable optical adhesives such as,for example, Norland NOA 72.

Electrical conductor layer 308 may comprise a plurality of heaterelectrodes 210 connected to the various thin-film heaters 212 a and 212b of thin-film heater layer 310. Heater electrodes 210 may include PCRsection leads 318, a PCR section common lead 316 a, thermal melt sectionleads 320, and a thermal melt section common lead 316 b. According toone embodiment of the present invention, one of the PCR section leads318 is connected to one end of each of the thin-film PCR heaters 212 a.A PCR common lead 316 a is connected to the other end of each of the PCRheaters 212 a. Similarly, one of the thermal melt section leads 320 andthermal melt section common lead 316 b is connected to either end ofeach thermal melt heater 212 b. While FIG. 3 shows the electricalconductor layer 308 and the heater layer 310 as separate layers, itwould be understood by one of ordinary skill in the art that they couldalso comprise the same layer.

According to some embodiments of the present invention, the thin-filmheater layer can be resistive materials of Pt, Al, Al₂N₃, Ni, ITO,Ni/chromium, etc.

In one embodiment, a platinum thin-film heater is used with depositionthickness in the range of approximately 10 to 5000 Angstroms, or morepreferably within the range of approximately 50 to 1000 Angstroms.Typical heater film resistance values range from approximately 200 to800 μΩ-cm, or approximately 20 to 1000Ω total resistance, or preferablyapproximately 50 to 250Ω total resistance. The exact composition ofthin-film heater material can be optimized by taking into account thepeak drive currents, overall trace resistances achievable, and designstability/durability.

Another alternate embodiment could incorporate the thin-film heaterresistor layer and a separate nearby resistor trace for measuring thenearby heat by the TCR characteristics of the resistor layer.

The heater electrodes 210, including PCR section leads 318, thermal meltsection leads 320, and common leads 316 a and 316 b, can be composed ofvarious materials ordinarily used as thin-film electrodes such as, forexample, Al, Ag, Au, Pt, Cu, etc. Electrode formation can be, forexample, by evaporation with a desired shape, size, and thickness. Theelectrodes can also be prepared by conventional sputtering process suchas, for example, in an Ar gas atmosphere.

In one embodiment, a protective layer 312 separates the thin film heaterlayer 310 from the substrate layer 314. The protective layers 306 and312 may be made from SiO₂ and can be prepared by conventional plasmaCVD, or sputtering. The SiO₂ thickness can range from approximately 1-3μm. A film layer made of Si:N can be formed by conventional plasma CVD.In one embodiment, the protective layer facilitates microchannelbiocompatibility to enable efficient PCR processes by isolating thereaction channel from the thin-film heaters 212 a and 212 b and theheater electrodes 210.

FIG. 4 shows a partial view of microfluidic device 200 showing a singlechannel 202 in detail. As illustrated in FIG. 4, the single channel 202includes the channel layer 302, the heater electrodes 210, thin filmheater 212 and protective layer 306. The microfluidic channel and thinfilm heater can be created having suitable dimensions for performing PCRand high resolution thermal melt reactions. In one exemplary embodiment,the microfluidic channel 202 dimensions can be approximately 10 μm×180μm and the thin-film heater 212 beneath the microfluidic channel 202 canbe approximately 150 μm wide at the bottom of the channel. Othermicrofluidic channel dimensions can be used as well such as, forexample, approximately 10 μm×300 μm, or more. Other thin film heaterdimensions could be used such as, for example, from approximately 30 μmwide to 300 μm wide (i.e. the full width of the channel in oneembodiment), or more.

FIG. 4 shows a portion of the device 200 at which a thin-film heater 212is overlapped by one of the electrodes 210. Other embodiments may alsoinclude dual thin-film heaters running down the channel in parallel.Such a design would be optimized at normalizing the thermal temperaturedistribution within the microfluidic channel 202.

Referring now to FIG. 5, a functional block diagram of a system 500 forusing a microfluidic device 200 is illustrated. The DNA sample is inputin the microfluidic chip 200 from a preparation stage 502. Thepreparation stage 502 may comprise appropriate devices for preparing thesample 504 and for adding one or more reagents 506 to the sample. Oncethe sample is input into the microfluidic chip 200, e.g., at an inputport 203 or via sipper tube 208, it flows through a channel 202 into thePCR zone 204 where PCR takes place. That is, as explained in more detailbelow, as the sample flows within a channel 202 through the PCR zone204, it is exposed to the temperature profile as shown in FIG. 1 aplurality of times to effect PCR amplification. Next, the sample flowsinto the thermal melt zone 206 where a high resolution thermal meltprocess occurs. Flow of sample into the microfluidic chip 200 can becontrolled by a flow controller 508. A control system 550 may comprise aflow controller 508, a PCR zone temperature controller 510, a PCR flowmonitor 518, a thermal melt zone temperature controller 524, and a zonefluorescence measurement system 532.

The temperature in the PCR zone 204 can be controlled by the PCR zonetemperature controller 510. The PCR zone temperature controller 510,which may be a programmed computer or other microprocessor, sendssignals to the heater device 512 (e.g., a PCR heater 212 a) based on thetemperature determined by a temperature sensor 514 (such as, forexample, an RTD or thin-film thermistor, or a thin-film thermocouplethermometer). In this way, the temperature of the PCR zone 204 can bemaintained at the desired level. According to some embodiments of thepresent invention, the PCR zone 204 may also be cooled by a coolingdevice 516 (for example, to quickly bring the channel temperature from92° C. down to 55° C.), which may also be controlled by the PCR zonetemperature controller 510. In one embodiment, the cooling device 516could be a peltier device, heat sink or forced convection air cooleddevice.

The flow of sample through the microfluidic channels 202 can be measuredby a PCR zone flow monitoring system 518. In one embodiment, the flowmonitoring system can be a fluorescent dye diffusion imaging andtracking system illustrated in U.S. patent application Ser. No.11/505,358, incorporated herein by reference. According to oneembodiment of the present invention, the channels in the PCR zone can beexcited by an excitation device 520 and light fluoresced from the samplecan be detected by a detection device 522. An example of one possibleexcitation device and detection device forming part of an imaging systemis illustrated in U.S. patent application Ser. Nos. 11/606,006 and11/505,358, incorporated herein by reference.

The thermal melt zone temperature controller 524, e.g. a programmedcomputer or other microprocessor, can be used to control the temperatureof the thermal melt zone 206. As with the PCR zone temperaturecontroller 510, the thermal melt zone temperature controller 524 sendssignals to the heating component 526 (e.g., a thermal melt heater 212 b)based on the temperature measured by a temperature sensor 528 which canbe, for example an RTD or thin-film thermocouple. Additionally, thethermal melt zone 206 may be independently cooled by cooling device 530.The fluorescent signature of the sample can be measured by the thermalmelt zone fluorescence measurement system 532. The fluorescencemeasurement system 532 excites the sample with an excitation device 534,and the fluorescence of the sample can be detected by a detection device536. An example of one possible fluorescence measurement system isillustrated in U.S. patent application Ser. Nos. 11/606,006 and11/505,358, incorporated herein by reference.

In accordance with aspects of the present invention, the thin filmheaters 212 function as both heaters and temperature detectors. Thus, inone embodiment of the present invention, the functionality of heatingelement 512 and 526 and temperature sensors 514 and 528 can beaccomplished by the thin film heaters 212.

In one embodiment, the system 500 sends power to the thin-film heaters212 a and/or 212 b, thereby causing them to heat up, based on a controlsignal sent by the PCR zone temperature controller 510 or the thermalmelt zone temperature controller 524. The control signal can be a pulsewidth modulation (PWM) control signal, as shown in FIG. 6. It isadvantageous to use a PWM signal to control the heaters 212, becausewith a PWM control signal, the same voltage potential across the heatersmay be used for all of the various temperatures required. As shown inFIG. 6, the desired temperature for the heaters is reached by changingthe duty cycle of the control signal. For example, the duty cycle of thecontrol signal for achieving 95° C. in a PCR heater might be about 50%as shown in the first curve in FIG. 6. As the desired temperaturedecreases, so does the duty cycle. For example, when the desiredtemperature is 72° C., the duty cycle might be around 25% as shown inthe third curve of FIG. 6. When the desired temperature is 55° C., theduty cycle might be only around 10%, as shown in the second curve ofFIG. 6.

According to one embodiment of the present invention, each thin-filmheater 212 a or 212 b can be independently controlled. Independentcontrol of the thin-film heaters permits the various heaters to besupplied with different amounts of power which may be desired tomaintain the desired set temperature. For instance, in a non-limitingexample, the edge-most heaters of the device 200 may require more powerthan the inner most heaters in order to maintain the same temperature.Individual control of the heaters also has the advantage of allowing theheaters to be multiplexed, as illustrated in FIGS. 7 and 8. Multiplexingthe thin-film heaters 212 allows for a balanced energy drain from thepower source and mitigates heat build up in the substrate 314.

As shown in FIG. 7, the heater signals may be multiplexed one after theother in succession. For instance, the falling edge of the control pulsefor microfluidic channel 1 may occur at the same time or after therising edge for channel 2's control pulse, and the rising edge forchannel 3's control pulse could occur at the same time or after thefalling edge of channel 2's control pulse and so on. In anotherembodiment, as shown in FIG. 8, several of the channels may be driven atthe same time. For instance, FIG. 8 shows channels 1, 3, 5 and 7 beingdriving at the same time and channels 2, 4, 6 and 8 being driven at thesame time. While a 50/50 duty cycle is shown for illustration purposesonly, actual duty cycles would change based on the desired temperature.FIG. 9 shows the representative thermal response to the differentialdrive method whereby the CH1 and CH2 channels are thermally out ofphase. Such a method is aimed at distributing the thermal energy withPWM so that the base temperature rise of the substrate chip material isminimized.

Individual microfluidic devices 200 can vary from chip to chip. Thus, toimprove the temperature set-point accuracy for each chip, the controlsystem for the microfluidic device 200 can be calibrated. As shown inFIG. 10, according to one embodiment of the present invention, a method1000 for calibrating a microfluidic device prior to use is provided. Themicrofluidic device is first inserted into the system 500 at step 1002.The control system 550 then applies a constant current to all of theheater electrodes 210 at step 1004. Next, at step 1006, the voltage dropacross each of the thin-film heaters 212 can then be measured todetermine individual resistance (R) values. Using the individual Rvalues, a nominal heater power (P) can be determined to achieve therequired channel temperatures for each microfluidic channel 202 at step1008. Next, the nominal power P is applied to each of the thin-filmheaters for a predetermined time at step 1010. In one embodiment, thepredetermined time can be from approximately 5 us to 30 ms, and ispreferably approximately 100 μs.

The temperature of the thin-film heater 212 a or 212 b is next monitoredby measuring the changing resistance as the thin-film heater 212 coolsat step 1012. From the data collected at step 1012, a thermal decay timeconstant for each thin film heater 212 can then be calculated at step1014 and an optimal PWM modulation frequency can be calculated based onthe thermal decay time constant at step 1016. The thermal decay timeconstant may be determined, for example, by taking two or moretemperature readings separated in time after heating power is stopped.With the heating power off, the temperature of the heater will begin todrop. The initial rate of temperature decay, in terms of degrees perunit time, may be calculated, for example, from two data points throughsimple algebra, through three or more data points by linear regression,or to many data points through a more complex model through curvefitting. Then, the digital drive signal to the heater should be adjustedto be at a high enough frequency to result in an acceptably small dropin temperature between consecutive pulses. The thermal decay timeconstant values are then stored in memory at step 1018. The calibrationmethod can be used to calibrate the control system 550 for both the PCRzone 204 and the thermal melt zone 206.

In one embodiment, the calibration pulse time is between approximately10 μs to 10 ms, more preferably between approximately 200 μs to 2 ms,and most preferably approximately 500 μs. The heater electroderesistance measurement collection time is between approximately 1 μs to1000 μs, more preferably between approximately 10 μs to 100 μs, and mostpreferably approximately 25 μs. The sampling rate for collecting theheater electrode resistance measurements is between approximately 0.1 μsto 1000 μs, more preferably between approximately 1 μs to 10 μs, andmost preferably approximately 2.5 μs.

FIG. 11 illustrates a method of temperature cycling 1100 to achieve PCRusing calibration data collected using method 1000. Calibration data1102 is retrieved from memory at step 1104. At step 1106, theappropriate PWM signal (based on the calibration data) is next appliedto each of the heater electrodes to achieve the desired temperature ofthe current PCR step. At step 1110, the temperature of the heaters ismeasured and compared to the desired temperature for the current PCRstep 1108 and the PWM modulation parameters 1112. According to oneembodiment, the temperature can be measured between PWM pulses asdescribed below. At step 1114, it is determined whether the appropriatetemperature has been achieved. If it has not been achieved, then themethod returns to step 1106. If it has been achieved, then the PWMsignal is adjusted to maintain the temperature for the appropriate holdtime for the current PCR step at step 1118 using the PCR step hold time1116 and the PWM modulation parameters 1120. At step 1122, the methoddetermines whether the appropriate hold time has been achieved. If thehold time has not been achieved, then the method returns to step 1118.If the appropriate hold time has been achieved, then, at step 1124, themethod indexes to the next PCR step. At step 1126, it is determinedwhether an entire PCR cycle has been completed. If not, then the methodreturns to step 1106. If it has been completed, then the methoddetermines whether the appropriate number of cycles have been completedand returns to step 1104 if not.

In addition to heating the microfluidic channel 202, thin film heaters212 a and 212 b can measure the temperature of the microfluidicchannels. To do so, the thin film heaters 212 a and/or 212 b arepreferably constructed from a material with an electrical resistancethat changes with temperature, such as platinum, Al, ITO, Cu, Ni and Nialloys. Thus, temperature can be derived from the determined resistanceof the heater. The measured temperature can be used in a closed loopfeedback controller.

In one embodiment, the power delivered to the thin-film heaters 212 ismodulated using a digital transistor switch instead of an analogvoltage. As illustrated in FIG. 12, digital transistor switch 1206 maybe a FET, and preferably may be a MOSFET. The control system varies theduty cycle (i.e., pulse width) of the drive signal to regulate powerdelivered to the thin-film heaters. When the transistor 1206 is ON, thecontrol circuit can measure the current delivered to the heat trace R2(comprising the PCR or thermal melt leads 318 or 320, a thin film heater212 a or 212 b, and a common lead 316 a or 316 b and represented as R2in FIG. 12). By knowing the current and voltage across the trace R2,control system 550 can calculate the impedance of R2. Next, the controlsystem can use a formula (e.g., Callendar-Van Dusen) to convert theimpedance value to a temperature value so the control system 550 canmove and hold the temperature as required for the PCR assay.

It may, however, also be desirable to measure the current when thetransistor is OFF. This is because when the transistor is in the ONstate the thin-film heaters 212 heat up very rapidly, and the thin-filmheaters 212 may be several degrees hotter than the fluid in themicrofluidic channels 202. If the system overshoots the desiredtemperature and the water forms micro bubbles in the channel, thecontrol system has difficulty because there is an insulating gas layerbetween its sensor and the load which causes a delay in feedbackcontrol.

Another problem with the gas bubble is it has the potential to greatlyexpand causing flow to be uncontrollable in the microchannels.

Thus, in accordance with another aspect of the present invention, animproved design allows temperature measurement when the transistor is inboth the OFF and ON states. In one embodiment, this can be accomplishedby having a small current flowing through R2 even when the transistor isOFF. A drive system for permitting temperature measurement when thetransistor is in both the OFF and ON states according to one embodimentof the present invention is illustrated in FIG. 12. In FIG. 12, aschematic of the PWM driver and measurement circuit 1200 is shown inwhich the transistor 1206 is connected to R2, which represents thecombined resistance of the thin-film heaters 212 a or 212 b and theleads connected to it (i.e. 316 a and 318 or 316 b and 320). The voltagedrop across R2 can be measured at measurement node 1202. The PWM drivesignal is sent to the gate of the transistor 1206 _(G) at drive signalnode 1204. A large value resistor R10 short circuits the drain 1206 _(D)and the source 1206 _(S). Preferably, R10 will be much larger (e.g., anorder of magnitude or more) than R2. When the transistor 1206 is ON,then current will flow through R2, substantially as normal, and thevoltage drop across R2 can be measured at measurement node 1202. Thevoltage drop across R2 can also be measured when the transistor 1206 isin the OFF state because of large value transistor R10 will allow asmaller current to flow through R2.

Due to the small current resulting from the large value of R10, the selfheating of R2 will be small, so the temperature measured by the trace R2will be close to the temperature of the fluid in the channel. Thecontrol system 550 can be configured to know when the transistor is ONand OFF, so it can use two different formulas to calculate thetemperature. For instance, when the transistor is ON, R9 and transistor1206 are in series and together are in parallel with R10, so the formulafor calculating the resistance of R2 is:

$\begin{matrix}{R_{2} = \frac{R_{{({9 + {RdsON}})}//10}\left( {V_{CC} - V_{measured}} \right)}{V_{measured}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where R_((9+RdsON)//10) represents the equivalent resistance of R10, R9and the resistance of the transistor 1206.

When the transistor is OFF, R10 is in series with R2, so the formula is:

$\begin{matrix}{R_{2} = \frac{R_{10}\left( {V_{CC} - V_{measured}} \right)}{V_{measured}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where V_(measured) is measured at node 1202.

From the resistance of trace R2, the temperature of R2 can be determinedby, e.g., applying the Callendar-Van Dusen equation, and the temperatureof R2 can be used in a control loop for regulating power to the heater.

Because the microfluidic device 200 can have more than one microfluidicchannel, channel cross talk can be an issue during OFF measurements.That is, if the power to one heater is off while power to an adjacentheater is on, there may be thermal and electrical cross talk between theheater(s) with power on and the heater(s) with power off, therebyaffecting the temperatures derived for the power-off heaters. Eachchannel still needs individual control to maintain an even temperaturedistribution among the PCR area. The potential for crosstalk can beminimized by configuring the control system to make sure all channelsare in the same state during the OFF measurements, as shown in FIG. 13.For example, according to one embodiment, all of the channels can be ata fixed PWM repetition rate, with only the duty cycle of the controlsignal being different for each channel to control the power to eachchannel. A maximum duty cycle (e.g., 90 percent) can be set and allchannels can be measured in the FET OFF state in the remaining time(e.g., 10 percent). Similarly, a minimum duty cycle of 10% could be usedto measure all channels in the FET ON state.

According to one embodiment of the present invention, the controller 550can use a PID feedback equation to change the power output to theheaters 212 a, 212 b to meet the power requirements for the PCR profile.In order to use PID feedback, the system can first be calibrated bysetting the output to a fixed power level and measuring the temperature.This can be done at several temperatures to develop an equation forvoltage to temperature conversion. Alternatively, the Callendar-VanDusen equation, as set forth below, may be used:

R _(T) =R(0° C.)(1+AT+BT ²)  Equation 3

where B is zero for the operating range to the microfluidic device 200.The equation thus can be solved for temperature as follows:

$\begin{matrix}{T = \frac{R_{T} - R_{0}}{{AR}_{0}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Where A is found by the following equation:

$\begin{matrix}{A = \frac{{R\left( {100{^\circ}\mspace{14mu} {C.}} \right)} - {R\left( {0{^\circ}\mspace{14mu} {C.}} \right)}}{100\; {R\left( {0{^\circ}\mspace{14mu} {C.}} \right)}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Typically, for platinum wires, A≈0.004.

Once the system is calibrated, the temperature can be measured by thecontroller 550 and the PID feedback equation can be used to change thepower to meet the desired PCR profile. The PID feedback equation isgiven by:

Output=K _(p)Error+K _(i)∂Error(dt)+K _(d) d(Error)/dt  Equation 6

The coefficients Kp, Ki, and Kd can be determined by a temperature stepresponse.

According to some embodiments, the heater controller 550 is a firstorder system with no time delay, so K_(d)=0. Kp=1/(Ba*τ) where τ is thetime it takes a heater 212 a or 212 b to cool from a hot temperature toa cool temperature and Ba is the system gain. According to someembodiments, the hot temperature is 95° C. and the cool temperature is54° C. Preferably, τ is about 0.4 and the system gain is about 2.5. Kican be set to the τ to provide moderate control speeds with littleovershoot. For more aggressive speeds, Ki can be set to some fraction ofτ such as τ/5, though doing so may result in the system havingover/undershoot. According to an alternative embodiment of the presentinvention, τ can be the time a heater 212 a or 212 b takes to heat upfrom a cool temperature (e.g. 54° C.) to a hot temperature (95° C.).

As stated above, the heater signals can be multiplexed in differentways. Multiplexing a plurality of heater control signals results in aresistance network such as that shown in FIG. 14, for example. FIG. 14represents the resistance network of an 8-channel microfluidic deviceaccording to one embodiment. In addition to the resistance of theplurality of thin-film heaters 212 a and 212 b (in this example: x1, x2,. . . , x8), there exists a number of parasitic resistances such as, forexample, xc for the common leads 316 a or 316 b and xδ for each of thespaces in 316 a and 316 b that separate thin-film heaters 212 a and 212b. With only independent measurements made at points 1-8, the system maybe underdetermined due to the common lead 316 a or 316 b and otherparasitic resistances. Specifically, even with only 8 measurements theparasitic resistances may result in measurement errors due to system andenvironmental factors. A further aspect of the present inventionutilizes a novel electrical measurement and drive circuit that candetermine the temperature of such multiplexed resistive heaters.

According to embodiments of the present invention, PCR thermocycling isachieved by using resistive traces (such as, for example, platinum thinfilms) as thin film heaters 212 a, 212 b. Thin film heaters can also actas resistance temperature detectors (RTDs). As described above, toachieve fast response and increased measurement sensitivity, eachheating element can be switched into separate “drive” or “measurement”states through the use of a switch (such as a transistor, relay, etc.).

The “drive” state uses a lower resistance sense resistor in the voltagedivision circuit to maximize the current through the resistive heaterand achieve fast heating rates. The “drive” state may or may not be usedin conjunction with pulse width modulation (PWM). The “drive” state isalso referred to as the “power on” state. The “measurement” state uses amoderate sense resistance to maximize measurement sensitivity (whileminimizing self heating). The “measurement” state is also referred to asthe “power-off” state.

In one embodiment of the present invention, two more switches perresistive heater are added as well as a common power supply switch thatin combination allow for greater measurement flexibility and efficacy.Additionally, “open” and “supply” states are added to each channel.Furthermore, the common power supply may be included in the “open” or“closed” configuration. These modifications allow the power supply to bemoved from the common lead to any lead desired. This allows the commonlead parasitic resistance to be removed from the measurement in certainconfigurations. Further, by making additional measurements the parasiticresistances can be explicitly determined, which removes a potentialmeasurement error.

A representative drive circuit 1500 capable of making these measurementsis illustrated in FIG. 15. In this embodiment, switching is accomplishedwith electric switches (1502, 1504, 1506, 1508, 1510, 1512), which canbe Metal Oxide Semiconductor Field Effect Transistors (MOSFET) switchesthat are driven by digital output lines on a high speed data acquisitionsystem. FETs 1508 and 1512 have specifically been included as levelshifting devices to increase the voltage at the gate of the primaryswitching FETs 1506 and 1510, respectively, which results in lower ONresistance switching and higher quality measurements. FIG. 15 shows thecircuit for only one of the eight resistive heaters (e.g., resistiveheater 1514) and the common lead.

Circuit branch 1513 may comprise electric switch 1512 and 1510 and maybe used to connect or disconnect the common lead to or from power source1518. Circuit branch 1507 includes electric switches 1506 and 1508 andcan connect or disconnect resistive heater 1514 to or from the drivecircuit branch 1503. Drive circuit branch 1503 is similar to the circuitshown in FIG. 12. Measurement circuit branch 1505 includes electricswitch 1504 and shunt resistor R187, which acts as a shunt around switch1504 when switch 1504 is OFF. With the transistor 15040N, the resistancemeasurements can be taken as normal. When transistor 1504 is OFF,however, then resistance measurements can still be taken due to thesmall current that still flows through large resistor R187.

Each of the remaining heater channels RZ1-10 to RZ2-16 also includescircuit branch 1507, drive circuit branch 1503 and measurement circuitbranch 1505. With drive circuit 1500, the common lead can bedisconnected from the power sources, each heater channel can beselectively connected to the power source, and each heater channel canbe selectively removed from the resistive network. Drive circuit 1500thus allows for isolated, power-on and power-off measurements.

With a plurality of channels the measurement combination possibilitiesare immense. In one embodiment, measurements can be made for the seriesresistance of any two resistors (common lead included), where the numberof combinations is given by:

$\begin{matrix}{C = \frac{\left( {n + 1} \right)!}{2 \cdot {\left( {n - 1} \right)!}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

where n is the number of thin film heaters 212 (common lead excluded).The actual number of measurements required can be determined by personsof ordinary skill given their need for accuracy and the limitations ofthe data logging system.

Considering a resistive network with 8 heating elements (as shown inFIG. 14), resistance measurements of a subset of all of the possiblemeasurements can be represented with a measurement matrix, such as A,which is shown below. The columns of A denote resistances, and the rowsdenote individual measurements. The product of A with the resistancevector x is equal to the measurements made during thermal control,vector b.

Ax=b  Equation 8

x=inv(A)b  Equation 9

Where:

$A = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 7 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 6 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 4 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 3 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 2 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{bmatrix}$ $X = \begin{bmatrix}x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & x_{6} & x_{7} & x_{8} & x_{c} & x_{\delta}\end{bmatrix}^{\prime}$

b=vector of measurements recorded through data acquisition

The individual resistances x can be determined through matrix inversion.However, the great flexibility of the measurement circuit and thisalgorithm allows for more measurements than unknowns, resulting in anoverdetermined system. This overdetermined system can then be solved foran optimal solution that reduces the effect of random measurementerrors. In one typical embodiment, the linear least squares technique isused to determine the optimal solution yielding estimates for all heaterresistances along with the parasitic resistances xc and xδ. Finally,each resistor's resistance versus temperature calibration curve(typically of the form R(T)=R(T₀)(1+αΔT)) is used to determine itstemperature, where R(T)=resistance at temperature T, R(T₀)=resistance attemperature T₀ and α=the temperature coefficient of resistivity of theparticular material.

The subset of resistance measurements may be taken according to avariety of different methods. FIGS. 16-21 illustrate several of themethods for taking resistance measurements in accordance with variousembodiments. In method 1600 illustrated in FIG. 16, each resistance ofeach heater 212 a or 212 b can be measured in series with the commonlead 316 a or 316 b, at step 1602. Next, at step 1604, the power supplyV_(CC) is disconnected from the common lead. The power supply is thenconnected to heater n−1, and the voltage drop is measured at heater n atstep 1606. Next, at step 1608 a system of linear equations for 8 heaterresistances and 1 parasitic resistance can be solved. Each resister's Rvs. T calibration data is used to determine the temperature of theresistor at step 1610.

FIG. 17 illustrates a method 1700 in which, at step 1702, each of theheaters 212 a or 212 b is measured in series with the common lead 316 aor 316 b. The power supply is then disconnected from the common lead atstep 1704. Next, at step 1706, the power supply is connected to heater 1and the voltage drop is measured at the n^(th) heater. At step 1708, thepower supply is then connected to the (n−1) th heater and the voltagedrop at heater n is measured. Next, at step 1710, a system of linearequations for 8 heater resistances and 2 parasitic resistances can besolved. At step 1712, each resistor's R vs. T calibration can then beused to determine the temperature.

FIG. 18 illustrated method 1800 in which, at step 1802, each heater ismeasured in series with the common lead. At step 1804, the power supplyis then disconnected from the common lead and a counter variable i isset to 1. At step 1806, the power supply is then connected to heater iand the voltage is measured at heater i+1. At step 1808, it isdetermined whether i+1=n. If not, then the counter is incremented andthe next measurements are taken at step 1806. If i+1 is equal to n, thenthe over determined system can be solved with optimization techniques atstep 1810. Finally, at step 1812, each resistor's R vs. T calibration isused to determine its temperature.

FIG. 19 illustrates method 1900 which is similar to method 1800 butincludes additional steps. As in the method illustrated in FIG. 18, eachheater is measured in series with the common lead at step 1902. Thepower supply is then disconnected from the common lead at step 1904, andi is set to equal 1. Next, at step 1906, the power supply is connectedto heater i, and the voltage drop at heater i+1 is measured. This isrepeated until i+1=n, as shown at step 1908. If not, then i isincremented and step 1906 is repeated. If i+1 does equal n, then i isreset to one and the power supply is connected to heater i+1 and thevoltage drop at heater i is measured at step 1910. This is repeated fori=1 to n. At step 1912, it is determined whether i+1=n. If not, i isincremented by 1 and the process returns to step 1910. Otherwise, theprocess continues to step 1914. At step 1914, the overdetermined systemcan be solved with optimization techniques. Finally, at step 1916, eachresistor's R vs. T calibration can be used to determine its temperature.

FIG. 20 illustrates method 2000 which can be characterized in that itkeeps the power supply connected to the same heater such as, forexample, heater n. First, each heater is measured in series with thecommon lead at step 2002. Next, at step 2004, the power supply isdisconnected from the common lead, and i is set to 1. Next, the powersupply is connected to heater n, and the voltage drop is measured acrossheaters 1 through n−1 at steps 2006 and 2008. The over-determined systemcan then be solved with optimization techniques, as shown in step 2010.Finally, each resistor's R vs. T calibration can be used to determineits temperature at step 2012.

FIG. 21 illustrates method 2100 in which, at step 2102, each heater ismeasured in series with the common lead. The power supply is thendisconnected from the common lead and a counter variable i is set to 1at step 2104. The power supply is then connected to heater i and thevoltage is measured at heater i+1 at step 2106. At step 2108, it isdetermined whether i+1=n. If not, then the counter is incremented by twoand the next measurements are taken at step 2106. If i+1 is equal to n,then the over determined system can be solved with optimizationtechniques at step 2110. Finally, at step 2112, each resistor's R vs. Tcalibration is used to determine its temperature.

In one embodiment, illustrated in FIG. 22, PWM and PID are used for bothPCR and thermal melt. In this case, different supply voltages, dutycycles, and PID control parameters (the proportional, integral, andderivative terms) can be implemented for the two different processes.For example, a larger supply voltage (e.g. 20 Volts) may be desired forPCR to effect faster response time, while a more modest voltage may bedesired for high resolution thermal melt (HRTm) (e.g. 10 Volts) toensure accurate temperature measurement. The duty cycles required wouldbe determined by the closed loop PID control system and could range from0 to 100%. For example, for the transition from denaturation toannealing (e.g. 95° C. to 55° C.), the duty cycle might initially bereduced to 0% to achieve rapid cooling. The duty cycle would then beincreased as the heater temperature approaches the set point, with theexact values determined using PID. Similarly, for the transition fromthe annealing to extension phases (e.g. 55° C. to 72° C.), the dutycycle might initially be set to 100% to heat quickly. The duty cyclewould then be reduced as the set point is approached.

FIG. 22 illustrates a method 2200 of PWM closed loop control of theheaters 212 a or 212 b according to an embodiment of the presentinvention. The method could be used to control the heaters in either thePCR zone 204 (PCR Cycles, Power Supply=20V) or the thermal melt zone 206(high resolution thermal melt, Power Supply=10V). At step 2201, the dutycycle is set to some initial value (e.g., 50%) and the PWM frequency isalso set to an initial value (e.g., 1 kHz). The FET or FETs can then beturned ON at step 2202 and the voltage across the heaters 212 a or 212 bmeasured at step 2204. The ON equation (equation 1, above), can then beused to calculate R2 (see FIG. 12). Next, at 2208, a determination ismade as to whether the FET has been ON long enough for the specifiedduty cycle. If yes, at steps 2210-2214, the FET is turned off, thevoltage drop across the heater 212 a or 212 b can be measured, and theOFF equation (equation 2, above) can be used to determine the value ofR2. At step 2216, the Callendar-Van Dusen equation can be used toconvert R into temperature factoring in the calibration coefficients2220, which may be downloaded from a storage device. Next, at step 2218,a new duty cycle can be calculated using a PID equation factoring in thelast duty cycle 2222, the temperature set point 2224, the error betweenthe set point and the measured temperature 2226, and the controlcoefficients Kp, Ki, and Kd 2228. Finally, the FET is turned back on forthe new duty cycle as control loops back to step 2202.

Alternatively, in another embodiment, closed loop control could be used,but PWM drive could be replaced with analog drive in which heating iscontrolled by varying the voltage rather than the duty cycle. Forexample, FIG. 23 illustrates method 2300 which is an analog closed loopcontrol used to obtain the desired temperature. In accordance with thisembodiment, after start at step 2301, the FET is turned on at step 2302.The power supply voltage is then set to an initial level at 2304. Thevoltage drop across the heater is measured at step 2306 and the ONequation (equation 1, above) is used to find R2 value at step 2308.Next, at step 2316, the Callendar-Van Dusen equation is used to convertthe resistance value into temperature factoring in the calibrationcoefficients 2320. Next, at step 2318, a PID equation is used tocalculate a new supply voltage factoring in the last supply voltage2322, the temperature set point 2324, the error between the temperatureset point and the measured temperature 2326, and control coefficients2328. The new supply voltage is set as control loops back to step 2302.

According to an alternative embodiment, after step 2308, the FET isturned OFF for a fixed amount of time to allow the sensor and the liquidin the microfluidic channel to equalize in temperature at step 2310. Thevoltage drop across the heater is measured at step 2312, and the OFFequation (equation 2, above) is used to calculate R2 at step 2314.

In another embodiment, closed loop control is utilized which involvesusing PWM to heat different resistive heaters differently to account formanufacturing variations or temperature gradients. As illustrated inFIG. 24, different duty cycles could be used for each heater to ensuretemperature uniformity. According to method 2400, the PWM frequency isset to a predetermined frequency (e.g., 1 kHz) at step 2401. Eachchannel's duty cycle is adjusted for uniform temperature at 2402. Next,at step 2404, the supply voltage is set to an initial value. The voltagedrop across the heater is then measured at step 2406, and the ONequation is used to calculate the value of R2 at step 2408. The FET iskept on until the duty cycle time is complete, as determined at step2410. Next, at step 2412, the FET is turned OFF and the voltage dropacross the heater is measured at step 2414. Next, the OFF equation canbe used in step 2416 to find R2. The Callendar-Van Dusen equation canthen be used to convert the resistance value measured for R2 into atemperature value at step 2418 factoring in calibration coefficients2422.

Finally, a PID equation is used to calculate a new supply voltage atstep 2420 factoring in the last supply voltage 2424, the temperaturesetpoint 2426, the error between the temperature setpoint and themeasured temperature 2428, and the control coefficients (Kp, Ki, andKd). The new supply voltage is set as the control loops back to step2404.

In another embodiment, closed loop control could be used for the PCRprocess (as described above), and thermal melt could be performed in anopen loop configuration. As illustrated in FIG. 25, a method of openloop thermal melting would involve increasing the supply voltage througha controllable power supply while monitoring the temperature of theheaters using the measurement control circuit. Another method of openloop thermal melting would involve ramping the duty cycles (e.g. from30% to 80%) while monitoring the temperature of the heaters 212 a, 212b.

In another embodiment, PCR could be performed in open loop configurationwhile thermal melt is performed using PID. For PCR, different drivecurrents and/or duty cycles would be used to achieve differenttemperatures. The different drive currents (which are predetermined) maybe achieved by a programmable power supply or through the use of adigital potentiometer (Rdp), which controls the total resistance andthus the drive current. The PCR drive voltage could be always on (100%duty cycle, i.e. traditional direct current (DC)) or PWM could be usedwith fixed but predetermined duty cycles less than 100%. In thisconfiguration, PWM could also be used to heat different resistiveheaters 212 a, 212 b differently to account for manufacturing variationsor temperature gradients.

According to another embodiment of the present invention, open loopcontrol can be performed by the method 2500 illustrated in FIG. 25. Inthis embodiment, the control signal is given an initial duty cycle(e.g., 50%) at step 2501. Next, at step 2502, the FET is turned ON andthe voltage drop across the heater is measured at step 2504. The ONequation can then be used to determine the value of R2 at step 2506. TheFET is held in the ON state until the appropriate amount of time for theduty cycle has passed, as determined at step 2508. Next, at step 2510,the FET is turned to the OFF state and the voltage drop across theheater is measured at step 2512. The OFF equation can then be used todetermine the value of R2 at step 2514. Callendar-Van Dusen equationscan then be used to convert R2's resistance value into a temperaturevalue in step 2516 using the heater's calibration coefficients 2522.Next, the actual temperatures can be recorded in step 2518, and the dutycycle and/or the analog voltage can be adjusted according to apredetermined power profile in step 2520. The FET is then turned ONagain as control loops back to step 2502.

Embodiments of the present invention have been fully described abovewith reference to the drawing figures. Although the invention has beendescribed based upon these preferred embodiments, it would be apparentto those of skill in the art that certain modifications, variations, andalternative constructions could be made to the described embodimentswithin the spirit and scope of the invention.

1. A method for determining the temperature of each of a plurality ofmultiplexed heater electrodes, wherein the heater electrodes are part ofa multiplex circuit sharing a common lead connecting the electrodes to apower supply, said method comprising: a. with the power supply connectedto the common lead, independently measuring a voltage drop of eachheater electrode in series with the common lead and storing a commonpower voltage drop data for each of the heater electrodes; b.disconnecting the power supply from the common lead; c. connecting thepower supply to each of one or more of the heater electrodes, whereinthe power supply is connected to one or more of the heater electrodes ata time; d. while the power supply is connected to a heater electrode,isolating at least one other heater electrode from all other heaterelectrodes of the multiplex circuit except the heater electrodeconnected to power supply, measuring an isolated voltage drop at eachisolated heater electrode, and storing isolated voltage drop data foreach isolated heater electrode; e. computing the resistance of each ofthe plurality of multiplexed heater electrodes by solving for theresistance of each heater electrode based at least in part on the storedcommon power voltage drop data and the stored isolated voltage dropdata; and f. deriving the temperature of each of the plurality ofmultiplexed heater electrodes from the computed resistance of eachelectrode.
 2. The method of claim 1, wherein the multiplex circuitcomprises n heater electrodes, step (c) comprises connecting the powersupply to heater electrode n−1, and step (d) comprises isolating heaterelectrode n and measuring an isolated voltage drop at heater electroden.
 3. The method of claim 2, wherein step (e) comprises solving a linearsystem of equations for the resistance of each of the plurality ofheater electrodes and a parasitic resistance of the common lead.
 4. Themethod of claim 1, wherein the multiplex circuit comprises n heaterelectrodes, step (c) comprises connecting the power supply to heaterelectrode 1, and step (d) comprises isolating heater electrode n andmeasuring an isolated voltage drop at heater electrode n, and whereinthe method further comprises, prior to performing steps (e) and (f)repeating step (c) for heater electrode n−1 and then repeating step (d)for heater electrode n.
 5. The method of claim 4, wherein step (e)comprises solving a linear system of equations for the resistance ofeach of the plurality of heater electrodes, a parasitic resistance ofthe common lead, and the sum of the parasitic resistances of all heaterelectrode channels.
 6. The method of claim 1, wherein the multiplexcircuit comprises n heater electrodes, step (c) comprises sequentiallyconnecting the power supply to each heater electrode i, wherein i=1 to(n−1), and step (d) comprises, for each heater electrode connected tothe power supply, isolating heater electrode i+1 and measuring anisolated voltage drop at heater electrode i+1.
 7. The method of claim 6,wherein step (e) comprises solving an overdetermined system withoptimization techniques.
 8. The method of claim 1, wherein the multiplexcircuit comprises n heater electrodes, step (c) comprises sequentiallyconnecting the power supply to each heater electrode i, wherein i=1 to(n−1), and step (d) comprises, for each heater electrode connected tothe power supply, isolating heater electrode i+1 and measuring anisolated voltage drop at heater electrode i+1, and wherein the methodfurther comprises, prior to performing steps (e) and (f), repeating step(c) by sequentially connecting the power supply to each heater electrodei+1, wherein i=1 to (n−1) and then repeating step (d) by, for eachheater electrode i+1 connected to the power supply, isolating heaterelectrode i and measuring an isolated voltage drop at heater electrodei.
 9. The method of claim 8, wherein step (e) comprises solving anoverdetermined system with optimization techniques.
 10. The method ofclaim 1, wherein the multiplex circuit comprises n heater electrodes,step (c) comprises connecting the power supply to heater electrode n,and step (d) comprises, while heater electrode n is connected to thepower supply, sequentially isolating heater electrode i, wherein i=1 to(n−1) and measuring an isolated voltage drop at each heater electrode i.11. The method of claim 10, wherein step (e) comprises solving anoverdetermined system with optimization techniques.
 12. The method ofclaim 1, wherein the multiplex circuit comprises n heater electrodes,step (c) comprises sequentially connecting the power supply to everyother heater electrode i, wherein i=1 to (n−1) incremented by 2, andstep (d) comprises, for each heater electrode i connected to the powersupply, isolating heater electrode i+1 and measuring an isolated voltagedrop at each heater electrode i+1.
 13. The method of claim 12, whereinstep (e) comprises solving an overdetermined system with optimizationtechniques.
 14. The method of claim 1, wherein power applied to a heaterelectrode is regulated by varying the duty cycle of a pulse widthmodulation (PWM), and wherein measuring a voltage drop at a heaterelectrode comprises: a. applying a fixed voltage across a heater channelincluding the heater electrode, a switching element for selectivelyopening or closing the channel to define the duty cycle, and a highresistance shunt around the switching element; b. closing the channelwith the switching element for a period time corresponding to a power-onportion of a desired duty cycle and passing current to the heaterelectrode through the closed switch and the shunt; c. while the circuitis closed, measuring a power-on voltage drop across the heaterelectrode; d. opening the circuit with the switching element for periodof time corresponding to a power-off portion of the desired duty cycle,and passing current to the heater electrode exclusively through theshunt; and e. while the circuit is opened, measuring a power-off voltagedrop across the heater electrode.
 15. A microfluidic device forperforming biological reactions comprising: a microfluidic chip having aplurality of microfluidic channels and a plurality of multiplexed heaterelectrodes, wherein the heater electrodes are part of a multiplexcircuit including a common lead connecting the heater electrodes to apower supply, each of the heater electrodes being associated with one ofthe microfluidic channels; and a control system configured to regulatepower applied to each heater electrode by varying a duty cycle, thecontrol system being further configured to determine the temperatureeach heater electrode by determining the resistance of each heaterelectrode.
 16. The microfluidic device of claim 15, wherein the controlsystem is further configured to selectively switch the power supply fromthe common lead to one or more of the heater electrodes to measureparasitic resistance within the multiplex circuit.
 17. The microfluidicdevice of claim 15, further comprising switching elements associatedwith each heater electrode and wherein the control system is furtherconfigured to control the switching elements to selectively remove oneor more heater elements from the multiplex circuit to facilitateisolated measurements of voltage drops across one or more heaterelements.
 18. The microfluidic device of claim 17, wherein the switchingelements comprise transistors.
 19. The microfluidic device of claim 17,wherein the switching elements comprise a primary switch and a levelshifting switch to minimize the resistance of the primary switch. 20.The microfluidic device of claim 17, wherein the control system isfurther configured to heat the heater electrodes by pulse widthmodulation.
 21. A method for determining the temperature of each of aplurality of multiplexed heater electrodes, wherein the heaterelectrodes are part of a multiplex circuit sharing a common leadconnecting the electrodes to a power supply, said method comprising: a.disconnecting the power supply from the common lead; b. connecting thepower supply to each of one or more of the heater electrodes, whereinthe power supply is connected to one or more of the heater electrodes ata time; c. while the power supply is connected to a heater electrode,isolating at least one other heater electrode from all other heaterelectrodes of the multiplex circuit except the heater electrodeconnected to power supply, measuring an isolated voltage drop at eachisolated heater electrode, and storing isolated voltage drop data foreach isolated heater electrode; d. computing the resistance of each ofthe plurality of multiplexed heater electrodes by solving for theresistance of each heater electrode; and e. deriving the temperature ofeach of the plurality of multiplexed heater electrodes from the computedresistance of each electrode.
 22. The method of claim 20, wherein themultiplex circuit comprises n heater electrodes, step (b) comprisesconnecting the power supply to heater electrode n−1, and step (c)comprises isolating heater electrode n and measuring an isolated voltagedrop at heater electrode n.
 23. The method of claim 22, wherein step (d)comprises solving a linear system of equations for the resistance ofeach of the plurality of heater electrodes and a parasitic resistance ofthe common lead.
 24. The method of claim 21, wherein the multiplexcircuit comprises n heater electrodes, step (b) comprises connecting thepower supply to heater electrode 1, and step (c) comprises isolatingheater electrode n and measuring an isolated voltage drop at heaterelectrode n, and wherein the method further comprises, prior toperforming steps (d) and (e) repeating step (b) for heater electrode n−1and then repeating step (c) for heater electrode n.
 25. The method ofclaim 24, wherein step (d) comprises solving a linear system ofequations for the resistance of each of the plurality of heaterelectrodes, a parasitic resistance of the common lead, and the sum ofthe parasitic resistances of all heater electrode channels.
 26. Themethod of claim 21, wherein the multiplex circuit comprises n heaterelectrodes, step (b) comprises sequentially connecting the power supplyto each heater electrode i, wherein i=1 to (n−1), and step (c)comprises, for each heater electrode i connected to the power supply,isolating heater electrode i+1 and measuring an isolated voltage drop atheater electrode i+1, and then making at least one more measurement withthe power supply connected to a given heater electrode and measuringisolated voltage drop at a different electrode.
 27. The method of claim26, wherein step (d) comprises solving an overdetermined system withoptimization techniques.
 28. The method of claim 21, wherein themultiplex circuit comprises n heater electrodes, step (b) comprisessequentially connecting the power supply to each heater electrode i,wherein i=1 to (n−1), and step (c) comprises, for each heater electrodei connected to the power supply, isolating heater electrode i+1 andmeasuring an isolated voltage drop at heater electrode i+1, and whereinthe method further comprises, prior to performing steps (d) and (e),repeating step (b) by sequentially connecting the power supply to eachheater electrode i+1, wherein i=1 to (n−1) and then repeating step (c)by, for each heater electrode i+1 connected to the power supply,isolating heater electrode i and measuring an isolated voltage drop atheater electrode i.
 29. The method of claim 28, wherein step (d)comprises solving an overdetermined system with optimization techniques.30. The method of claim 21, wherein the multiplex circuit comprises nheater electrodes, step (b) comprises connecting the power supply toheater electrode n, and step (c) comprises, while heater electrode n isconnected to the power supply, sequentially isolating heater electrodei, wherein i=1 to (n−1) and measuring an isolated voltage drop at eachheater electrode i, and then making at least one more measurement withthe power supply connected to a given heater electrode and measuringisolated voltage drop at a different electrode.
 31. The method of claim30, wherein step (d) comprises solving an overdetermined system withoptimization techniques.
 32. The method of claim 21, wherein themultiplex circuit comprises n heater electrodes, step (b) comprisessequentially connecting the power supply to every other heater electrodei, wherein i=1 to (n−1) incremented by 2, and step (c) comprises, foreach heater electrode i connected to the power supply, isolating heaterelectrode i+1 and measuring an isolated voltage drop at each heaterelectrode i+1.
 33. The method of claim 32, wherein step (d) comprisessolving an overdetermined system with optimization techniques.
 34. Themethod of claim 21, wherein power applied to a heater electrode isregulated by varying the duty cycle through pulse width modulation(PWM), and wherein measuring a voltage drop at a heater electrodecomprises: a. applying a fixed voltage across a heater channel includingthe heater electrode, a switching element for selectively opening orclosing the channel to define the duty cycle, and a high resistanceshunt around the switching element; b. closing the channel with theswitching element for a period time corresponding to a power-on portionof a desired duty cycle and passing current to the heater electrodethrough the closed switch and the shunt; c. while the circuit is closed,measuring a power-on voltage drop across the heater electrode; d.opening the circuit with the switching element for period of timecorresponding to a power-off portion of the desired duty cycle, andpassing current to the heater electrode exclusively through the shunt;and e. while the circuit is opened, measuring a power-off voltage dropacross the heater electrode.